1. Field of the Invention
This invention relates to the field of acoustic navigation systems, and more particularly relates to a system of this type having improved accuracy over short-baseline and super-short-baseline navigation systems.
2. Brief Description of the Prior Art
The objective of navigation is to estimate, in real-time, the position, relative to a tracking platform, of one or more cooperative targets in a known reference frame. Navigation systems estimate the positions of targets by measuring the round-trip time delay between the transmission of an interrogation pulse from the tracking platform and the reception of reply signals (by hydrophones at the tracking platform) from the interrogated, cooperative target. Acoustic navigation systems are typically categorized into three groups: long-; short-; and super-short-baseline configurations. The difference is associated with the distance between the elements receiving reply signals from the object/target being tracked/located. Long-baseline systems typically involve sensors placed hundreds to thousands of feet separated on the ocean bottom. Platform-based navigation has conventionally been performed in one of two ways: short-baseline (SBL) navigation; and super-short-baseline (SSBL) navigation.
In short-baseline navigation, receiver elements, i.e. hydrophones, are mounted in different locations on the platform. The spacing between receiver elements is typically tens or hundreds of wavelengths at the signal frequency. In underwater acoustic navigation, the tracking platform is typically a surface ship or a submarine. In radar navigation, the platform may be a ship, a land vehicle, or an airplane. In satellite navigation, the earth itself is the usual reference platform. The short-baseline platform receiver elements detect replies from cooperative targets and convert the signals into a form that can be processed by the navigation system processor. The processor determines the relative time delay between signal arrivals at the different receiver elements. The position of each target, relative to the platform, is then calculated from the time-difference-of-arrival (TDOA) estimates. The cooperative target sometimes use a spread-spectrum reply signal to allow for a more precise measurement of time-delay.
For super-short-baseline (SSBL) navigation, all the receiver elements are mounted in an array where the separation is less than one-half the wavelength at the reply signal frequency. The direction-of-arrival is determined by calculating the relative phase difference between the received hydrophone signals. Since the elements in the hydrophone array are separated by one-half wavelength or less, the phase differences are less than one half cycle, and each phase difference can be directly converted to a time difference without ambiguity. The position of the cooperative target is then estimated from the time differences. This type of navigation system is popular, because the small array requires very little space for installation. The accuracy of super short baseline navigation is limited, however, because the baseline lengths are so short. Small errors in the phase differences used to estimate time-delay result in large errors in the direction-of-arrival estimate. In addition, the elements of the super-short-baseline array are in such close proximity that they may shadow each other for certain signal arrival directions.
The position estimation performance of each of these techniques depends upon the accuracy of the time-difference-of-arrival estimation. For short baseline navigation, the time-difference-of-arrival is estimated by cross-correlating each pair of received signals. Burdick states in "Underwater Acoustic Systems Analysis, second edition, pg. 383, that the variance of a time-delay estimate .sigma..sub..tau. is bounded below by the following formula: ##EQU1## where E is the signal energy, N.sub.0 is the noise spectral density, and .beta..sub.0 is the RMS signal bandwidth. This equation shows that to minimize the variance, it is desirable to use a wide bandwidth signal with high energy (high power and long duration to maximize the energy).
For super-short-baseline navigation, the time-difference-of-arrival is obtained by estimating the relative phase between each pair of channels. For a continuous wave (CW) pulse, the variance in the phase estimate .sigma..sub..phi. is bounded below by the following formula: ##EQU2##
Provided there is no phase ambiguity, the standard deviation of the phase estimate is converted into a standard deviation in the time-delay estimate .sigma..sub..tau..sbsb..phi. by the following formula: ##EQU3## where f.sub.c is the carrier frequency of the CW pulse. These lower bounds on time-difference-of-arrival estimation correspond to the following RMS bearing estimation errors for the direction-of-arrival .theta..
Cross-Correlation-Based Error in Bearing Estimate
The standard deviation of the bearing estimate .sigma..sub..theta. using cross-correlation-based techniques is: ##EQU4## where d is the separation between receiver elements, and c is the speed of wave propagation in the medium.
Phase-Difference-Based Error in Bearing Estimate
The standard deviation of the bearing estimate .sigma..sub..theta. obtained using a phase-difference-based technique is: ##EQU5## The carrier frequency is always larger than the RMS bandwidth, so the standard deviation in bearing angle obtained with the phase difference technique is always smaller than that obtained with the cross-correlation-based technique. However, when any pair of elements is separated by more than one-half wavelength, the phase difference is ambiguous (by .+-.2.pi., .+-.4.pi., etc) and products an ambiguous time-difference-of-arrival. This phase ambiguity must be resolved before the phase difference can be used for precise time-delay estimation.
To derive accurate position estimates, besides the appropriate phase and time differences, one also must know the signal propagation speed very accurately. The relative motion between the tracking platform and the targets must also be known. For good signal quality, the received signals must be properly gated (windowed) to eliminate signal contamination by multipath signal reception, which will otherwise produce erroneous bearing estimates.
The propagation speed of the signal is an important parameter, because it is used in converting the time-difference-of-arrival estimate into a direction-of-arrival estimate .theta. using the following formula: ##EQU6## For small angles, a relative error in propagation speed corresponds to the same relative error in the direction-of-arrival estimate. Target and receiver motion in the propagating medium will affect the time-difference-of-arrival estimates and the perceived frequency of the received signals. When the phase difference estimation is converted into a time-difference-of-arrival estimate, the received carrier frequency must be precisely known.
Multipath signals degrade the performance of short-baseline systems when they overlap in time with the direct-path signals. The direct-path reply signal will arrive at the receiver first, and for some interval of time will be the only signal received. Later, the first reflected-path signal will arrive and interfere with the direct-path signal. If the data, during the time period of interference, is used to estimate a single direction-of-arrival, it will be in error, because two or more signals were arriving from different angles during that time period.